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Experiments with a Crookes tube first demonstrated the
particle nature of electrons. In this illustration, the profile of
the cross-shaped target is projected against the tube face at right
by a beam of electrons.[1]

In many physical phenomena, such as electricity, magnetism, and thermal
conductivity, electrons play an essential role. An electron in
motion relative to an observer generates a magnetic field,
and will be deflected by external magnetic fields. When an electron
is accelerated, it can absorb or radiate energy in the form of
photons. Electrons, together with atomic nuclei made of protons and neutrons, make up atoms. However, electrons
contribute less than 0.06% to an atom's total mass. The attractive
Coulomb force
between an electron and a proton causes electrons to be bound into atoms.
The exchange or sharing of the electrons between two or more atoms
is the main cause of chemical bonding.[12]

History

The ancient
Greeks noticed that amber
attracted small objects when rubbed with fur; apart from lightning, this phenomenon
was humanity's earliest recorded experience with electricity.[13] In
his 1600 treatise De Magnete,
the English physician William Gilbert coined the New Latin term electricus, to refer to
this property of attracting small objects after being rubbed.[14] Both
electric and electricity are derived from the
Latin ēlectrum (also
the root of the alloy of the
same name), which came from the Greek word ήλεκτρον (ēlektron) for amber.

Between 1838 and 1851, British natural philosopher Richard Laming
developed the idea that an atom is composed of a core of matter
surrounded by subatomic particles that had unit electric
charges.[3]
Beginning in 1846, German physicist William Weber theorized that
electricity was composed of positively and negatively charged
fluids, and their interaction was governed by the inverse square law. After studying the
phenomenon of electrolysis in 1874, Irish physicist George Johnstone Stoney
suggested that there existed a "single definite quantity of
electricity", the charge of a monovalention. He was able to estimate the value of this
elementary charge e by means of Faraday's laws of
electrolysis.[15]
However, Stoney believed these charges were permanently attached to
atoms and could not be removed. In 1881, German physicist Hermann
von Helmholtz argued that both positive and negative charges
were divided into elementary parts, each of which "behaves like
atoms of electricity".[4]

In 1894, Stoney coined the term electron to represent
these elementary charges, saying, "... an estimate was made of the
actual amount of this most remarkable fundamental unit of
electricity, for which I have since ventured to suggest the name
electron."[16] The
English
name electron is a combination of the word
electric and the suffix -on, with the latter
now used to designate a subatomic particle, such as a proton or
neutron.[17][18]

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Discovery

The German physicist Johann Wilhelm Hittorf undertook
the study of electrical conductivity in rarefied gases. In 1869, he discovered a
glow emitted from the cathode that increased in size with decrease in
gas pressure. In 1876, the German physicist Eugen Goldstein
showed that the rays from this glow cast a shadow, and he dubbed
them cathode
rays.[20]
During the 1870s, the English chemist and physicist Sir William Crookes
developed the first cathode ray tube to have a high vacuum inside.[21]
He then showed that the luminescence rays appearing within the tube
carried energy and moved from the cathode to the anode. Furthermore, by applying a magnetic field,
he was able to deflect the rays, thereby demonstrating that the
beam behaved as though it were negatively charged.[22][23] In
1879, he proposed that these properties could be explained by what
he termed 'radiant matter'. He suggested that this was a fourth
state of matter, consisting of negatively charged molecules that were being
projected with high velocity from the cathode.[24]

The German-born British physicist Arthur Schuster expanded upon Crookes'
experiments by placing metal plates in parallel to the cathode rays
and applying an electric potential between the
plates. The field deflected the rays toward the positively charged
plate, providing further evidence that the rays carried negative
charge. By measuring the amount of deflection for a given level of
current,
in 1890 Schuster was able to estimate the charge-to-mass ratio of the ray
components. However, this produced a value that was more than a
thousand times greater than what was expected, so little credence
was given to his calculations at the time.[22][25]

In 1896, the British physicist J. J. Thomson, with his colleagues John S.
Townsend and H. A. Wilson,[6]
performed experiments indicating that cathode rays really were
unique particles, rather than waves, atoms or molecules as was
believed earlier. Thomson made good estimates of both the charge
e and the mass m, finding that cathode ray
particles, which he called "corpuscles," had perhaps one thousandth
of the mass of the least massive ion known: hydrogen.[11]
He showed that their charge to mass ratio, e/m,
was independent of cathode material. He further showed that the
negatively charged particles produced by radioactive materials, by
heated materials and by illuminated materials were universal.[26] The
name electron was again proposed for these particles by the Irish
physicist George F. Fitzgerald, and the name
has since gained universal acceptance.[22]

While studying naturally fluorescing minerals in 1896, the French
physicist Henri
Becquerel discovered that they emitted radiation without any
exposure to an external energy source. These radioactive
materials became the subject of much interest by scientists,
including the New
Zealand physicist Ernest Rutherford who discovered they
emitted particles. He designated these particles alpha and beta, on the basis
of their ability to penetrate matter.[27] In
1900, Becquerel showed that the beta rays emitted by radium could be deflected by an
electric field, and that their mass-to-charge ratio was the same as
for cathode rays.[28] This
evidence strengthened the view that electrons existed as components
of atoms.[29][30]

The electron's charge was more carefully measured by the
American physicist Robert Millikan in his oil-drop
experiment of 1909, the results of which he published in 1911.
This experiment used an electric field to prevent a charged droplet
of oil from falling as a result of gravity. This device could
measure the electric charge from as few as 1–150 ions with an error
margin of less than 0.3%. Comparable experiments had been done
earlier by Thomson's team, using clouds of charged water droplets
generated by electrolysis,[6]
and in 1911 by Abram
Ioffe, who independently obtained the same result as Millikan
using charged microparticles of metals, then published his results
in 1913.[31]
However, oil drops were more stable than water drops because of
their slower evaporation rate, and thus more suited to precise
experimentation over longer periods of time.[32]

Around the beginning of the twentieth century, it was found that
under certain conditions a fast moving charged particle caused a
condensation of supersaturated water vapor along its
path. In 1911, Charles Wilson used this
principle to devise his cloud chamber, allowing the tracks of
charged particles, such as fast-moving electrons, to be
photographed.[33]

Atomic
theory

The Bohr model of
the atom, showing states of electron with energy quantized by the
number n. An electron dropping to a lower orbit emits a photon
equal to the energy difference between the orbits.

By 1914, experiments by physicists Ernest Rutherford, Henry Moseley, James Franck and Gustav
Hertz had largely established the structure of an atom as a
dense nucleus
of positive charge surrounded by lower-mass electrons.[34]
In 1913, Danish physicist Niels Bohr postulated that electrons resided
in quantized energy states, with the energy determined by the
angular momentum of the electron's orbits about the nucleus. The
electrons could move between these states, or orbits, by the
emission or absorption of photons at specific frequencies. By means
of these quantized orbits, he accurately explained the spectral lines of
the hydrogen atom.[35]
However, Bohr's model failed to account for the relative
intensities of the spectral lines and it was unsuccessful in
explaining the spectra of more complex atoms.[34]

Chemical bonds between atoms were explained by Gilbert Newton Lewis, who in 1916 proposed
that a covalent
bond between two atoms is maintained by a pair of electrons
shared between them.[36]
Later, in 1923, Walter Heitler and Fritz London gave the
full explanation of the electron-pair formation and chemical
bonding in terms of quantum mechanics.[37]
In 1919, the American chemist Irving Langmuir elaborated on the
Lewis' static model of the atom and suggested that all electrons
were distributed in successive "concentric (nearly) spherical
shells, all of equal thickness".[38] The
shells were, in turn, divided by him in a number of cells each
containing one pair of electrons. With this model Langmuir was able
to qualitatively explain the chemical properties of all elements
in the periodic table,[37]
which were known to largely repeat themselves according to the periodic law.[39]

In 1924, Austrian physicist Wolfgang Pauli observed that the
shell-like structure of the atom could be explained by a set of
four parameters that defined every quantum energy state, as long as
each state was inhabited by no more than a single electron. (This
prohibition against more than one electron occupying the same
quantum energy state became known as the Pauli exclusion
principle.)[40] The
physical mechanism to explain the fourth parameter, which had two
distinct possible values, was provided by the Dutch physicists Abraham Goudsmith and George Uhlenbeck when they suggested that
an electron, in addition to the angular momentum of its orbit,
could possess an intrinsic angular momentum.[34][41] This
property became known as spin, and explained the previously
mysterious splitting of spectral lines observed with a
high-resolution spectrograph; this phenomenon is known as
fine structure
splitting.[42]

Quantum
mechanics

In his 1924 dissertation Recherches sur la théorie des quanta
(Research on Quantum Theory), French physicist Louis de
Broglie hypothesized that all matter possesses a De Broglie wave similar to light[43].
That is, under the appropriate conditions, electrons and other
matter would show properties of either particles or waves. The corpuscular properties of a
particle are demonstrated when it is shown to have a localized
position in space along its trajectory at any given moment.[44]
Wave-like nature is observed, for example, when a beam of light is
passed through parallel slits and creates interference patterns.
In 1927, the interference effect was demonstrated with a beam of
electrons by English physicist George Paget Thomson with a thin
metal film and by American physicists Clinton Davisson and Lester Germer using
a crystal of nickel.[45]

In quantum mechanics, the behavior of an electron in an atom is
described by an orbital, which is a probability
distribution rather than an orbit. In the figure, the shading
indicates the relative probability to "find" the electron, having
the energy corresponding to the given quantum numbers, at that point.

The success of de Broglie's prediction led to the publication,
by Erwin Schrödinger in 1926, of the Schrödinger equation that
successfully describes how electron waves propagated.[46]
Rather than yielding a solution that determines the location of an
electron over time, this wave equation can be used to predict the
probability of finding an electron near a position. This approach
was later called quantum mechanics, which provided an
extremely close derivation to the energy states of an electron in a
hydrogen atom.[47] Once
spin and the interaction between multiple electrons were
considered, quantum mechanics allowed the configuration of
electrons in atoms with higher atomic numbers than hydrogen to be
successfully predicted.[48]

In 1928, building on Wolfgang Pauli's work, Paul Dirac produced a
model of the electron - the Dirac equation, consistent with relativity theory, by applying
relativistic and symmetry considerations to the hamiltonian formulation
of the quantum mechanics of the electro-magnetic field.[49] In
order to resolve some problems within his relativistic equation, in
1930 Dirac developed a model of the vacuum as an infinite sea of
particles having negative energy, which was dubbed the Dirac sea. This led him to
predict the existence of a positron, the antimatter counterpart of the electron.[50] This
particle was discovered in 1932 by Carl D. Anderson,
who proposed calling standard electrons negatrons, and
using electron as a generic term to describe both the
positively and negatively charged variants. This usage of the term
'negatron' is still occasionally encountered today, and it may be
shortened to 'negaton'.[51][52]

With a beam energy of 1.5 GeV, the first high-energy
particle collider was ADONE, which
began operations in 1968.[56] This
device accelerated electrons and positrons in opposite directions,
effectively doubling the energy of their collision when compared to
striking a static target with an electron.[57] The
Large
Electron-Positron Collider (LEP) at CERN, which was operational from 1989 to 2000,
achieved collision energies of 209 GeV and made important
measurements for the Standard Model of particle physics.[58][59]

Characteristics

Classification

Standard Model of elementary particles. The electron is at lower
left.

In the Standard Model of particle physics, electrons belong to
the group of subatomic particles called leptons, which are believed to be fundamental or
elementary particles. Electrons
have the lowest mass of any charged lepton (or electrically charged
particle of any type) and belong to the first-generation of fundamental
particles.[60] The
second and third generation contain charged leptons, the muon and the tauon, which are identical to the electron in
charge, spin
and interactions, but are more
massive. Leptons differ from the other basic constituent of matter,
the quarks, by their lack of strong
interaction. All members of the lepton group are fermions,
because they all have half-odd integer spin; the electron has spin
1⁄2.[61]

Electrons have an electric charge of −1.602×10
−19coulomb,[7]
which is used as a standard unit of charge for subatomic particles.
Within the limits of experimental accuracy, the electron charge is
identical to the charge of a proton, but with the opposite
sign.[64] As
the symbol e is used for the elementary charge, the electron is
commonly symbolized by e−, where the minus
sign indicates the negative charge. The positron is symbolized by
e+ because it
has the same properties as the electron but with a positive rather
than negative charge.[7][61]

The electron has an intrinsic angular momentum or spin of 1⁄2.[7]
This property is usually stated by referring to the electron as a
spin-1⁄2
particle.[61]
For such particles the spin magnitude is √3⁄
2ħ.[note
3] while the result of the measurement of a
projection of the spin on any
axis can only be ±ħ⁄2.
In addition to spin, the electron has an intrinsic magnetic moment along
its spin axis.[7]
It is approximately equal to one Bohr magneton,[65][note 4]
which is a physical constant equal to 9.274 009 15(23) × 10−24joules per tesla.[7]
The orientation of the spin with respect to the momentum of the
electron defines the property of elementary particles known as helicity.[66]

The electron has no known substructure.[2][67]
Hence, it is defined or assumed to be a point particle with a point
charge and no spatial extent.[9]
Observation of a single electron in a Penning trap shows the upper limit of the
particle's radius is 10−22meters.[68] There
is a physical constant called the "classical electron radius",
with the much larger value of 2.8179×10
−15 m. However, the terminology comes from a
simplistic calculation that ignores the effects of quantum
mechanics; in reality, the so-called classical electron radius
has little to do with the true fundamental structure of the
electron.[69][note
5]

Quantum
properties

As with all particles, electrons can act as waves. This is
called the wave–particle duality and can be
demonstrated using the double-slit experiment. The
wave-like nature of the electron allows it to pass through two
parallel slits simultaneously, rather than just one slit as would
be the case for a classical particle. In quantum mechanics, the
wave-like property of one particle can be described mathematically
as a complex-valued function, the wave function,
commonly denoted by the Greek letter psi (ψ). When the absolute value of
this function is squared, it gives the probability that
a particle will be observed near a location—a probability density.[72]

Electrons are identical particles because they
cannot be distinguished from each other by their intrinsic physical
properties. In quantum mechanics, this means that a pair of
interacting electrons must be able to swap positions without an
observable change to the state of the system. The wave function of
fermions, including electrons, is antisymmetric, meaning that it
changes sign when two electrons are swapped; that is, ψ(r1,
r2) = −ψ(r2,
r1), where the variables
r1 and r2 correspond to the
first and second electrons, respectively. Since the absolute value
is not changed by a sign swap, this corresponds to equal
probabilities. Bosons, such as the photon, have symmetric
wave functions instead.[72]

In the case of antisymmetry, solutions of the wave equation for
interacting electrons result in a zero probability that each pair
will occupy the same location or state. This is responsible for the
Pauli exclusion principle,
which precludes any two electrons from occupying the same quantum
state. This principle explains many of the properties of electrons.
For example, it causes groups of bound electrons to occupy
different orbitals in an atom, rather than all
overlapping each other in the same orbit.[72]

Virtual
particles

Physicists believe that empty space may be continually creating
pairs of virtual particles, such as a positron and electron, which
rapidly annihilate
each other shortly thereafter.[73] The
combination of the energy variation needed to create these
particles, and the time during which they exist, fall under the
threshold of detectability expressed by the Heisenberg uncertainty relation,
ΔE·Δt ≥ ħ. In effect, the
energy needed to create these virtual particles, ΔE, can
be "borrowed" from the vacuum for a period of time, Δt,
so that their product is no more than the reduced Planck
constant, ħ ≈ 6.6×10
−16 eV·s . Thus, for a virtual electron,
Δt is at most 1.3×10
−21 s.[74]

A schematic depiction of virtual electron–positron pairs appearing
at random near an electron (at lower left)

While an electron–positron virtual pair is in existence, the coulomb force
from the ambient electric field surrounding an electron
causes a created positron to be attracted to the original electron,
while a created electron experiences a repulsion. This causes what
is called vacuum polarization. In effect, the
vacuum behaves like a medium having a dielectric permittivity more than unity.
Thus the effective charge of an electron is actually smaller than
its true value, and the charge decreases with increasing distance
from the electron.[75][76] This
polarization was confirmed experimentally in 1997 using the
Japanese TRISTAN particle accelerator.[77]
Virtual particles cause a comparable shielding effect for the mass
of the electron.[78]

The interaction with virtual particles also explains the small
(about 0.1%) deviation of the intrinsic magnetic moment of the
electron from the Bohr magneton (the anomalous magnetic moment).[65][79] The
extraordinarily precise agreement of this predicted difference with
the experimentally determined value is viewed as one of the great
achievements of quantum electrodynamics.[80]

In classical physics, the angular
momentum and magnetic moment of an object depend upon its physical
dimensions. Hence, the concept of a dimensionless electron
possessing these properties might seem inconsistent. The apparent
paradox can be explained by the formation of virtual
photons in the electric field generated by the electron. These
photons cause the electron to shift about in a jittery fashion
(known as zitterbewegung),[81] which
results in a net circular motion with precession. This motion produces both the
spin and the magnetic moment of the electron.[9][82] In
atoms, this creation of virtual photons explains the Lamb shift observed in
spectral lines.[75]

Interaction

An electron generates an electric field that exerts an
attractive force on a particle with a positive charge, such as the
proton, and a repulsive force on a particle with a negative charge.
The strength of this force is determined by Coulomb's inverse
square law.[83] When
an electron is in motion, it generates a magnetic field.[84]
The Ampère-Maxwell law relates the
magnetic field to the mass motion of electrons (the current) with
respect to an observer. It is this property of induction which
supplies the magnetic field that drives an electric
motor.[85] The
electromagnetic field of an arbitrary moving charged particle is
expressed by the Liénard–Wiechert potentials,
which are valid even when the particle's speed is close to that of
light (relativistic).

A particle with charge q (at left) is moving with velocity
v through a magnetic field B that is oriented
toward the viewer. For an electron, q is negative so it
follows a curved trajectory toward the top.

When an electron is moving through a magnetic field, it is
subject to the Lorentz force that exerts an influence in
a direction perpendicular to the plane defined by the magnetic
field and the electron velocity. This centripetal force causes the electron
to follow a helical trajectory
through the field at a radius called the gyroradius. The acceleration from this
curving motion induces the electron to radiate energy in the form
of synchrotron radiation.[86][87][note 6]
The energy emission in turn causes a recoil of the electron, known
as the Abraham-Lorentz-Dirac force, which creates
a friction that slows the electron. This force is caused by a
back-reaction of the electron's own field upon itself.[88]

In quantum electrodynamics the
electromagnetic interaction between particles is mediated by
photons. An isolated electron that is not undergoing acceleration
is unable to emit or absorb a real photon; doing so would violate
conservation of energy and momentum. Instead, virtual
photons can transfer momentum between two charged particles. It is
this exchange of virtual photons that, for example, generates the
Coulomb force.[89]
Energy emission can occur when a moving electron is deflected by a
charged particle, such as a proton. The acceleration of the
electron results in the emission of Bremsstrahlung radiation.[90]

Here, Bremsstrahlung is produced by an electron e
deflected by the electric field of an atomic nucleus. The energy
change E2 − E1
determines the frequency f of the emitted photon.

An elastic collision between a photon (light) and a solitary
(free) electron is called Compton scattering. This collision
results in a transfer of momentum and energy between the particles,
which modifies the wavelength of the photon by an amount called the
Compton
shift.[note 7]
The maximum magnitude of this wavelength shift is
h/mec, which is known as the Compton
wavelength.[91] For
an electron, it has a value of 2.43 × 10−12 m.[7]
When the wavelength of the light is long (for instance, the
wavelength of the visible light is 0.4–0.7 μm) the
wavelength shift becomes negligible. Such interaction between the
light and free electrons is called Thomson scattering or Linear Thomson
scattering.[92]

The relative strength of the electromagnetic interaction between
two charged particles, such as an electron and a proton, is given
by the fine-structure constant. This
value is a dimensionless quantity formed by the ratio of two
energies: the electrostatic energy of attraction (or repulsion) at
a separation of one Compton wavelength, and the rest energy of the
charge. It is given by α ≈ 7.297353×10
−3, which is approximately equal to 1⁄137.[7]

When electrons and positrons collide, they annihilate each other, giving rise to two
or more gamma ray photons. If the electron and positron have
negligible momentum, a positronium atom can form before
annihilation results in two or three gamma ray photons totalling
1.022 MeV.[93][94] On
the other hand, high-energy photons may transform into an electron
and a positron by a process called pair production, but only in the
presence of a nearby charged particle, such as a nucleus.[95][96]

In the theory of electroweak interaction, the left-handed component of electron's
wavefunction forms a weak isospin doublet with the electron neutrino. This means
that during weak interactions, electron neutrinos
behave like electrons. Either member of this doublet can undergo a
charged
current interaction by emitting or absorbing a W and be converted into the
other member. Charge is conserved during this reaction because the
W boson also carries a charge, canceling out any net change during
the transmutation. Charged current interactions are responsible for
the phenomenon of beta
decay in a radioactive atom. Both the electron
and electron neutrino can undergo a neutral current interaction via a Z0 exchange, and
this is responsible for neutrino-electron elastic
scattering.[97]

Atoms and
molecules

Probability densities for the first few hydrogen atom orbitals,
seen in cross-section. The energy level of a bound electron
determines the orbital it occupies, and the color reflects the
probability to find the electron at a given position.

An electron can be bound to the nucleus of an atom by
the attractive Coulomb force. A system of several electrons bound
to a nucleus is called an atom. If the number of electrons is
different from the nucleus' electrical charge, such an atom is
called an ion. The wave-like
behavior of a bound electron is described by a function called an
atomic
orbital. Each orbital has its own set of quantum numbers such
as energy, angular momentum and projection of angular momentum, and
only a discrete set of these orbitals exist around the nucleus.
According to the Pauli exclusion principal each orbital can be
occupied by up to two electrons, which must differ in their spin
quantum number.

Electrons can transfer between different orbitals by the
emission or absorption of photons with an energy that matches the
difference in potential.[98]
Other methods of orbital transfer include collisions with
particles, such as electrons, and the Auger effect.[99] In
order to escape the atom, the energy of the electron must be
increased above its binding energy to the atom.
This occurs, for example, with the photoelectric effect, where an
incident photon exceeding the atom's ionization energy is absorbed by the
electron.[100]

The orbital angular momentum of electrons is quantized. Because the electron is
charged, it produces an orbital magnetic moment that is
proportional to the angular momentum. The net magnetic moment of an
atom is equal to the vector sum of orbital and spin magnetic
moments of all electrons and the nucleus. The nuclear magnetic
moment is, however, negligible in comparison to the effect from the
electrons. The magnetic moments of the electrons that occupy the
same orbital (so called, paired electrons) cancel each other
out.[101]

The chemical
bond between atoms occurs as a result of electromagnetic
interactions, as described by the laws of quantum mechanics.[102] The
strongest bonds are formed by the sharing or transfer of electrons between atoms,
allowing the formation of molecules.[12]
Within a molecule, electrons move under the influence of several
nuclei, and occupy molecular orbitals; much as they can
occupy atomic orbitals in isolated atoms.[103] A
fundamental factor in these molecular structures is the existence
of electron
pairs. These are electrons with opposed spins, allowing them to
occupy the same molecular orbital without violating the Pauli
exclusion principle (much like in atoms). Different molecular
orbitals have different spatial distribution of the electron
density. For instance, in bonded pairs (i.e. in the pairs that
actually bind atoms together) electrons can be found with the
maximal probability in a relatively small volume between the
nuclei. On the contrary, in non-bonded pairs electrons are
distributed in a large volume around nuclei.[104]

Conductivity

A lightning discharge
consists primarily of a flow of electrons.[105] The
electric potential needed for lightning may be generated by a
triboelectric effect.[106][107]

If a body has more or fewer electrons than are required to
balance the positive charge of the nuclei, then that object has a
net electric charge. When there is an excess of electrons, the
object is said to be negatively charged. When there are fewer
electrons than the number of protons in nuclei, the object is said
to be positively charged. When the number of electrons and the
number of protons are equal, their charges cancel each other and
the object is said to be electrically neutral. A macroscopic body
can develop an electric charge through rubbing, by the triboelectric effect.[108]

Independent electrons moving in vacuum are termed free
electrons. Electrons in metals also behave as if they were free. In
reality the particles that are commonly termed electrons in metals
and other solids are quasi-electrons—quasi-particles,
which have the same electrical charge, spin and magnetic moment as
real electrons but may have a different mass.[109]
When free electrons—both in vacuum and metals—move, they produce a
net flow of charge
called an electric current, which generates a
magnetic field. Likewise a current can be created by a changing
magnetic field. These interactions are described mathematically by
Maxwell's equations.[110]

At a given temperature, each material has an electrical conductivity that
determines the value of electric current when an electric
potential is applied. Examples of good conductors include
metals such as copper and gold, whereas glass and Teflon are poor conductors. In
any dielectric
material, the electrons remain bound to their respective atoms and
the material behaves as an insulator. Most semiconductors have
a variable level of conductivity that lies between the extremes of
conduction and insulation.[111] On
the other hand, metals have an electronic band structure
containing partially filled electronic bands. The presence of such
bands allows electrons in metals to behave as if they were free or
delocalized electrons. These
electrons are not associated with specific atoms, so when an
electric field is applied, they are free to move like a gas (called
Fermi gas)[112]
through the material much like free electrons.

Because of collisions between electrons and atoms, the drift velocity of
electrons in a conductor is on the order of millimeters per second.
However, the speed at which a change of current at one point in the
material causes changes in currents in other parts of the material,
the velocity of
propagation, is typically about 75% of light speed.[113]
This occurs because electrical signals propagate as a wave, with
the velocity dependent on the dielectric
constant of the material.[114]

Metals make relatively good conductors of heat, primarily
because the delocalized electrons are free to transport thermal
energy between atoms. However, unlike electrical conductivity, the
thermal conductivity of a metal is nearly independent of
temperature. This is expressed mathematically by the Wiedemann-Franz law,[112]
which states that the ratio of thermal conductivity to the
electrical conductivity is proportional to the temperature. The
thermal disorder in the metallic lattice increases the electrical
resistivity of the
material, producing a temperature dependence for electrical
current.[115]

When cooled below a point called the critical temperature,
materials can undergo a phase transition in which they lose all
resistivity to electrical current, in a process known as superconductivity. In BCS theory, this behavior
is modeled by pairs of electrons entering a quantum state known as
a Bose–Einstein condensate.
These Cooper pairs
have their motion coupled to nearby matter via lattice vibrations
called phonons, thereby
avoiding the collisions with atoms that normally create electrical
resistance.[116]
(Cooper pairs have a radius of roughly 100 nm, so they can
overlap each other.)[117]
However, the mechanism by which higher temperature
superconductors operate remains uncertain.

Electrons inside conducting solids, which are quasi-particles
themselves, when tightly confined at temperatures close to absolute zero,
behave as though they had split into two other quasiparticles: spinons and holons.[118][119] The
former carries spin and magnetic moment, while the latter
electrical charge.

Motion and
energy

According to Einstein's theory of special
relativity, as an electron's speed approaches the speed of light,
from an observer's point of view its relativistic mass increases,
thereby making it more and more difficult to accelerate it from
within the observer's frame of reference. The speed of an electron
can approach, but never reach, the speed of light in a vacuum,
c. However, when relativistic electrons—that is, electrons
moving at a speed close to c—are injected into a
dielectric medium such as water, where the local speed of light is
significantly less than c, the electrons temporarily
travel faster than light in the medium. As they interact with the
medium, they generate a faint light called Cherenkov
radiation.[120]

Lorentz factor as a function of velocity. It starts at value 1 and
goes to infinity as v approaches c.

The effects of special relativity are based on a quantity known
as the Lorentz
factor, defined as
where v is the speed of the particle. The kinetic energy
Ke of an electron moving with velocity
v is:

where me is the mass of electron. For
example, the Stanford linear
accelerator can accelerate an electron to roughly
51 GeV.[121]
This gives a value of nearly 100,000 for γ, since the mass
of an electron is 0.51 MeV/c2. The
relativistic momentum of this electron is
100,000 times the momentum that classical mechanics would predict
for an electron at the same speed.[note
8]

Since an electron behaves as a wave, at a given velocity it has
a characteristic de
Broglie wavelength. This is given by
λe = h/p where
h is Planck's constant and p is the
momentum.[43]
For the 51 GeV electron above, the wavelength is about 2.4×10
−17 m, small enough to explore structures well
below the size of an atomic nucleus.[122]

Formation

The Big Bang theory is
the most widely accepted scientific theory to explain the early
stages in the evolution of the Universe.[123] For
the first millisecond of the Big Bang, the temperatures were over
10 billion Kelvin
and photons had mean energies over a million electron volts. These
photons were sufficiently energetic that they could react with each
other to form pairs of electrons and positrons,

where γ is a photon,
e+ is a positron
and e− is an
electron. Likewise, positron-electron pairs annihilated each other
and emitted energetic photons. An equilibrium between electrons,
positrons and photons was maintained during this phase of the
evolution of the Universe. After 15 seconds had passed, however,
the temperature of the universe dropped below the threshold where
electron-positron formation could occur. Most of the surviving
electrons and positrons annihilated each other, releasing gamma
radiation that briefly reheated the universe.[124]

For reasons that remain uncertain, during the process of leptogenesis there was an excess
in the number of electrons over positrons.[125]
Hence, about one electron in every billion survived the
annihilation process. This excess matched the excess of protons
over anti-protons, in a condition known as baryon
asymmetry, resulting in a net charge of zero for the
universe.[126][127] The
surviving protons and neutrons began to participate in reactions
with each other—in the process known as nucleosynthesis, forming isotopes of
hydrogen and helium, with
trace amounts of lithium.
This process peaked after about five minutes.[128] Any
leftover neutrons underwent negative beta decay with a half-life of about a
thousand seconds, releasing a proton and electron in the
process,

where n is a neutron,
p is a proton and νe is an
electron
antineutrino. For about the next 300,000–400,000 years,
the excess electrons remained too energetic to bind with atomic
nuclei.[129]
What followed is a period known as recombination, when neutral
atoms were formed and the expanding universe became transparent to
radiation.[130]

Roughly one million years after the big bang, the first
generation of stars began to
form.[130]
Within a star, stellar nucleosynthesis results
in the production of positrons from the fusion of atomic nuclei.
These antimatter particles immediately annihilate with electrons,
releasing gamma rays. The net result is a steady reduction in the
number of electrons, and a matching increase in the number of
neutrons. However, the process of stellar evolution can result in the
synthesis of radioactive isotopes. Selected isotopes can
subsequently undergo negative beta decay, emitting an electron and
antineutrino from the nucleus.[131] An
example is the cobalt-60
(60Co) isotope, which decays to form nickel-60
(60Ni).[132]

An extended air shower generated by an energetic cosmic ray
striking the Earth's atmosphere

When pairs of virtual particles (such as an electron and
positron) are created in the vicinity of the event horizon, the
random spatial distribution of these particles may permit one of
them to appear on the exterior; this process is called quantum tunneling. The gravitational potential of the
black hole can then supply the energy that transforms this virtual
particle into a real particle, allowing it to radiate away into
space.[134] In
exchange, the other member of the pair is given negative energy,
which results in a net loss of mass-energy by the black hole. The
rate of Hawking radiation increases with decreasing mass,
eventually causing the black hole to evaporate away until, finally,
it explodes.[135]

Cosmic rays are
particles traveling through space with high energies. Energy events
as high as 3.0 × 1020
eV have been recorded.[136]
When these particles collide with nucleons in the Earth's atmosphere, a shower of particles is
generated, including pions.[137]
More than half of the cosmic radiation observed from the Earth's
surface consists of muons. The
particle called a muon is a lepton which is produced in the upper
atmosphere by the decay of a pion. A muon, in turn, can decay to
form an electron or positron. Thus, for the negatively charged pion
π−,[138]

Observation

Remote observation of electrons requires detection of their
radiated energy. For example, in high-energy environments such as
the corona of a star, free
electrons form a plasma that radiates energy due to
Bremsstrahlung. Electron gas can undergo plasma
oscillation, which is waves caused by synchronized variations
in electron density, and these produce energy emissions that can be
detected by using radio telescopes.[140]

The frequency of a photon is proportional to its
energy. As a bound electron transitions between different energy
levels of an atom, it will absorb or emit photons at characteristic
frequencies. For instance, when atoms are irradiated by a source
with a broad spectrum, distinct absorption lines will appear in the
spectrum of transmitted radiation. Each element or molecule
displays a characteristic set of spectral lines, such as the hydrogen spectral series. Spectroscopic
measurements of the strength and width of these lines allow the
composition and physical properties of a substance to be
determined.[141][142]

In laboratory conditions, the interactions of individual
electrons can be observed by means of particle detectors, which allow
measurement of specific properties such as energy, spin and
charge.[100]
The development of the Paul trap and Penning trap allows
charged particles to be contained within a small region for long
durations. This enables precise measurements of the particle
properties. For example, in one instance a Penning trap was used to
contain a single electron for a period of 10 months.[143]
The magnetic moment of the electron was measured to a precision of
eleven digits, which, in 1980, was a greater accuracy than for any
other physical constant.[144]

The first video images of an electron's energy distribution were
captured by a team at Lund University in Sweden, February
2008. The scientists used extremely short flashes of light, called
attosecond pulses, which allowed an
electron's motion to be observed for the first time.[145][146]

The distribution of the electrons in solid materials can be
visualized by angle resolved
photoemission spectroscopy (ARPES). This technique employs the
photoelectric effect to measure the reciprocal space—a mathematical
representation of periodic structures that is used to infer the
original structure. ARPES can be used to determine the direction,
speed and scattering of electrons within the material.[147]

Plasma
applications

Particle
beams

Electron beams
are used in welding,[149]
which allows energy densities up to 107 W·cm−2
across a narrow focus diameter of 0.1–1.3 mm and usually does not
require a filler material. This welding technique must be performed
in a vacuum, so that the electron beam does not interact with the
gas prior to reaching the target, and it can be used to join
conductive materials that would otherwise be considered unsuitable
for welding.[150][151]

Electron beam lithography
(EBL) is a method of etching semiconductors at resolutions smaller
than a micron.[152]
This technique is limited by high costs, slow performance, the need
to operate the beam in the vacuum and the tendency of the electrons
to scatter in solids. The last problem limits the resolution to
about 10 nm. For this reason, EBL is primarily used for the
production of small numbers of specialized integrated
circuits.[153]

Particle accelerators use electric
fields to propel electrons and their antiparticles to high
energies. As these particles pass through magnetic fields, they
emit synchrotron radiation. The intensity of this radiation is spin
dependent, which causes polarization of the electron beam—a process
known as the Sokolov–Ternov effect.[note 9]
The polarized electron beams can be useful for various experiments.
Synchrotron
radiation can also be used for cooling the electron beams, which
reduces the momentum spread of the particles. Once the particles
have accelerated to the required energies, separate electron and
positron beams are brought into collision. The resulting energy
emissions are observed with particle detectors and are studied in
particle
physics.[157]

Imaging

Low-energy electron
diffraction (LEED) is a method of bombarding a crystalline
material with a collimated beam of electrons, then
observing the resulting diffraction patterns to determine the
structure of the material. The required energy of the electrons is
typically in the range 20–200 eV.[158] The
reflection high
energy electron diffraction (RHEED) technique uses the
reflection of a beam of electrons fired at various low angles to
characterize the surface of crystalline materials. The beam energy
is typically in the range 8–20 keV and the angle of incidence
is 1–4°.[159][160]

The electron microscope directs a
focused beam of electrons at a specimen. As the beam interacts with
the material, some electrons change their properties, such as
movement direction, angle, relative phase and energy. By recording
these changes in the electron beam, microscopists can produce
atomically resolved image of the material.[161] In
blue light, conventional optical microscopes have a
diffraction-limited resolution of about 200 nm.[162] By
comparison, electron microscopes are limited by the de Broglie wavelength
of the electron. This wavelength, for example, is equal to
0.0037 nm for electrons accelerated across a 100,000-volt potential.[163] The
Transmission
Electron Aberration-corrected Microscope is capable of
sub-0.05 nm resolution, which is more than enough to resolve
individual atoms.[164]
This capability makes the electron microscope a useful laboratory
instrument for high resolution imaging. However, electron
microscopes are expensive instruments that are costly to
maintain.

There are two main types of electron microscopes: transmission and scanning. Transmission
electron microscopes function in a manner similar to overhead
projector, with a beam of electrons passing through a slice of
material then being projected by lenses on a photographic slide
or a charge-coupled device. In
scanning electron microscopes, the image is produced by rastering a finely
focused electron beam, as in a TV set, across the studied sample.
The magnifications range from 100× to 1,000,000× or higher for both
microscope types. The scanning tunneling
microscope uses quantum tunneling of electrons from a sharp
metal tip into the studied material and can produce atomically
resolved images of its surface.[165][166][167]

Other

In the free electron laser (FEL), a relativistic electron beam
is passed through a pair of undulators containing arrays of dipole magnets,
whose fields are oriented in alternating directions. The electrons
emit synchrotron radiation, which, in turn, coherently interacts with the same
electrons. This leads to the strong amplification of the radiation
field at the resonance
frequency. FEL can emit a coherent high-brilliance electromagnetic radiation with a
wide range of frequencies, from microwaves to soft X-rays. These devices can
be used in the future for manufacturing, communication and various
medical applications, such as soft tissue surgery.[168]

^
The classical electron radius is derived as follows. Assume that
the electron's charge is spread uniformly throughout a spherical
volume. Since one part of the sphere would repel the other parts,
the sphere contains electrostatic potential energy. This energy is
assumed to equal the electron's rest energy, defined by
special
relativity (E=mc2).
From electrostatics theory, the potential
energy of a sphere with radius r and charge e
is given by:

where ε0 is the vacuum permittivity. For an
electron with rest mass m0, the rest energy is
equal to:

where c is the speed of light in a vacuum. Setting them
equal and solving for r gives the classical electron
radius.
See: Haken, Hermann; Wolf, Hans
Christoph; Brewer, W. D. (2005). The Physics of Atoms and
Quanta: Introduction to Experiments and Theory. Springer.
p. 70. ISBN
3540208070.

^
The change in wavelength, Δλ, depends on the angle of the
recoil, θ, as follows,

where c is the speed of light in a vacuum and
me is the electron mass. See Zombeck
(2007:393,396).

^ Solving for the velocity of the
electron, and using an approximation for large γ, one
obtains:

^ The polarization of an electron
beam means that the spins of all electrons point into one
direction. In other words, the projections of the spins of all
electrons onto their momentum vector have the same sign.

^Murayama, Hitoshi (March 10–17, 2006).
"Supersymmetry Breaking Made Easy, Viable and Generic". Proceedings
of the XLIInd Rencontres de Moriond on Electroweak Interactions and
Unified Theories. La Thuile, Italy. arΧiv:0709.3041.—lists a 9% mass
difference for an electron that is the size of the Planck distance.

Contents

Description

The Niels Bohr model of the atom. Three electron shells about a nucleus, with an electron moving from the second to the first level and releasing a photon.

Electrons have the smallest electrical charge. When they move, they generate an electric current. An electron has a mass of about 1/1836 times a proton.[4]
Electrons in an atom exist in a number of electron shells surrounding the central nucleus. Each electron shell is given a number 1, 2, 3, and so on, starting from the one closest to the nucleus (the innermost shell). Each shell can hold up to a certain maximum number of electrons. The distribution of electrons in the various shells is called electronic arrangement (or electronic form or shape). Electronic arrangement can be shown by numbering or an electron diagram.

While most electrons are found in atoms, others move independently in matter, or together as cathode rays in a vacuum. In some superconductors, electrons move in pairs. When electrons flow, this flow is called electricity, or an electric current.

An object can be described as 'negatively charged' if there are more electrons than protons in an object, or 'positively charged' when there are more protons than electrons. Electrons can move from one object to another when touched. They may be attracted to another object with opposite charge, or repelled when they both have the same charge. When an object is 'grounded', electrons from the charged object go into the ground, making the object neutral. This is what lightning conductors do.

Chemical reactions

Electrons in their shells round an atom are the basis of chemical reactions. Complete outer shells, with maximum electrons, are less reactive. Outer shells with less than maximum electrons are reactive. The number of electrons in atoms is the underlying basis of the chemical periodic table.[5]

Measurement

Electric charge can be directly measured with a device called an electrometer. Electric current can be directly measured with a galvanometer. The measurement given off by a galvanometer is different from the measurement given off by an electrometer. Today laboratory instruments are capable of containing and observing individual electrons.

'Seeing' an electron

In laboratory conditions, the interactions of individual electrons can be observed by means of particle detectors, which allow measurement of specific properties such as energy, spin and charge.[6] In one instance a Penning trap was used to contain a single electron for a period of 10 months.[7] The magnetic moment of the electron was measured to a precision of eleven digits, which, in 1980, was a greater accuracy than for any other physical constant.[8]

The first video images of an electron's energy distribution were captured by a team at Lund University in Sweden, February 2008. The scientists used extremely short flashes of light, called attosecond pulses, which allowed an electron's motion to be observed for the first time.[9][10] The distribution of the electrons in solid materials can also be visualized.[11]

Anti-particle

The antiparticle of the electron is called a positron. This is identical to the electron, but carries electrical and other charges of the opposite sign. When an electron collides with a positron, they may scatter off each other or be totally annihilated, producing a pair (or more) of gamma rayphotons.

History of its discovery

The effects of electrons were known long before it could be explained. The Ancient Greeks knew that rubbing amber against fur attracted small objects. Now we know the rubbing strips off electrons, and that gives an electric charge to the amber.
Many physicists worked on the electron. J.J. Thomson proved it existed,[12] in 1897, but another man gave it the name 'electron'.[13]